When * SolvOpt* was developed, the goal was to design an algorithm
for smooth and non-smooth optimization problems, which combines efficiency,
robustness and accuracy. Many runs with testing functions known to be a
challenge for any optimization routine indicate that these design goals
have been achieved.

However, there is no optimization code which never fails. So, we do not
claim the robustness of the code in every case, but we claim that it works in 99 cases
from every 100.

Below we present the results of test runs with the default values for the optional parameters.
The standard starting points were used, unless stated otherwise.
Tables 1, 1a, 1b, 1c, 2, 2a, 2b, 2c, 3, 4, 5, 6 provide the results of test runs with the use
of the set of tests by Moré * et al*. These were obtained by use of `solvopt.m`.
The test M-functions are included to the *SolvOpt for use with Matlab*
distribution package.
The page Moré test functions
provides the data collected on these challenging minimization tests.

The first column of all the tables displays the title and the dimension
of the test function. The second column provides
the known local minimum. The third displays the function value at the solution
obtained by the M-function ` solvopt` with the default optional parameters.
The third column gives the relative error for the minimizer in terms of
the infinity (max) norm.
The numbers of function and gradient evaluations
are presented in columns 5 and 6 respectively.

- Table 1. The solution for the Moré
set of UNC-problems by SolvOpt
*with*user-supplied gradients. - Table 2. The solution the Moré
set of for UNC-problems by SolvOpt
*without*user-supplied gradients. - Table 1a. The solution for the Moré
set of UNC-problems by SolvOpt
*with*user-supplied gradients and*10-fold*standard starting points. - Table 2a. The solution the Moré
set of for UNC-problems by SolvOpt
*without*user-supplied gradients and*10-fold*standard starting points. - Table 1b. The solution for the Moré
set of UNC-problems by SolvOpt
*with*user-supplied gradients and*100-fold*standard starting points. - Table 2b. The solution for the Moré
set of UNC-problems by SolvOpt
*without*user-supplied gradients and*100-fold*standard starting points. - Table 1c. The solution for the Moré
set of UNC-problems by SolvOpt
*with*user-supplied gradients and*1000-fold*standard starting points. - Table 2c. The solution for the Moré
set of UNC-problems by SolvOpt
*without*user-supplied gradients and*1000-fold*standard starting points. - Table 3. The solution for the Moré
set of UNC-problems by SolvOpt at
`f`=10^{16}`f`_{0}*with*user-supplied gradients and standard starting points. - Table 4. The solution for the Moré
set of UNC-problems by SolvOpt at
`f`=10^{16}`f`_{0}*without*user-supplied gradients and standard starting points. - Table 5. The solution for the Moré
set of UNC-problems by SolvOpt at
`f`=10^{-8}`f`_{0}*with*user-supplied gradients and standard starting points. - Table 6. The solution for the Moré
set of UNC-problems by SolvOpt at
`f`=10^{-8}`f`_{0}*without*user-supplied gradients and standard starting points.

One can find some results on minimization of nonsmooth (penalty) functions in the manual.

The following table illustrate the performance of SolvOpt by solution
of some constrained test problems selected from the huge CUTE test set
(to learn more about the CUTE visit the URLs
ftp://130.246.8.61/pub/cute or
ftp://138.48.4.14/pub/cute .
One can also download the ANSI FORTRAN routines coded for these tests
from
ftp://plato.la.asu.edu/pub/donlp2.

In this table, the first column provides the title (identifier) of a
test problem, the second one displays the number of variables, the
numbers of equality and inequality constraints are found in the third and
the fourth columns respectively, the fifth column provides the function
value at the solution found and the other four columns display the values
for the counters: objective function values, gradients of the objective
function, maximal residuals for constraints and gradients for constraints
respectively.

These results were obtained by the FORTRAN subroutine ** solvopt**.

Table 7. The solution for constrained problems selected from the CUTE.